Strategic Decision-Making in Multiagent Domains: A Weighted Constrained Potential Dynamic Game Approach

In interactive multiagent settings, decision-making and planning are challenging mainly due to the agents' interconnected objectives. Dynamic game theory offers a formal framework for analyzing such intricacies. Yet, solving constrained dynamic games and determining the interaction outcome in the form of generalized Nash equilibria (GNE) pose computational challenges due to the need for solving constrained coupled optimal control problems. In this article, we address this challenge by proposing to leverage the special structure of many real-world multiagent interactions. More specifically, our key idea is to leverage constrained dynamic potential games, which are games for which GNE can be found by solving a single constrained optimal control problem associated with minimizing the potential function. We argue that constrained dynamic potential games can effectively facilitate interactive decision-making in many multiagent interactions. We will identify structures in realistic multiagent interactive scenarios that can be transformed into weighted constrained potential dynamic games (WCPDGs). We will show that the GNE of the resulting WCPDG can be obtained by solving a single constrained optimal control problem. We will demonstrate the effectiveness of the proposed method through various simulation studies and show that we achieve significant improvements in solve time compared to state-of-the-art game solvers. We further provide experimental validation of our proposed method in a navigation setup involving two quadrotors carrying a rigid object while avoiding collisions with two humans.

I. Introduction

Numerous robotic applications, such as autonomous driving, crowd–robot navigation, and delivery robots, include scenarios that require multiagent interactions. In these situations, a robot is tasked with engaging with either human individuals or other robots present in the surrounding environment. Making decisions and creating plans in these domains is challenging as agents in multiagent systems may have different goals or objectives. This requires agents to develop strategies that account for how other agents will react to their actions, i.e., each agent needs to reason about the likely reactions of other agents in their decision-making. Furthermore, agents may need to satisfy some task constraints, such as collision avoidance and goal constraints. Such reasoning may be computationally demanding, requiring agents to perform joint prediction and planning.